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euler_005.py
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euler_005.py
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import math
from euler import *
# What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?
def isDivisibleAll(number,max):
for x in range(2,max+1):
if number % x != 0:
return False
return True
def find005Answer():
x = 20
# likely candidate for 20 is 1,862,340,480.
# if reach >>2e9, something is wrong
dangerZone = 2e9 * 4
while True:
#test divisibility
if isDivisibleAll(x,20):
print("And the winner is... " + str(x))
print("Its factors are " + str(fact(x)))
return
if x > dangerZone:
print("Reached " + str(x) + " and didn't find it yet..")
return
# increment...
x = x+1
def find005AnswerFast():
# factorials by their nature are close to what is desired.
# E.g. we know that 5!=120 will be divisible by all the number from 1 to 5
# since it is by definition 1*2*3*4*5.
# The 20! is a LARGE number, but it's likely one of its factors meets the condition.
# I got lucky in the way that it met the condition of being the smallest such number
# (I didn't prove that it would be the case)
i = math.factorial(19)
for x in fact(i):
if isDivisibleAll(x,20):
print("And the winner is... " + str(x))
for k in range(2,21):
print(str(x) + " / " + str(k) + " = " + str(x/k))
print("Its factors are " + str(fact(x)))
return
print("not found")
find005AnswerFast()